E. De Schutter and J.G. Bjaalie- Coding in the Granular Layer of the Cerebellum

8/3/2019 E. De Schutter and J.G. Bjaalie- Coding in the Granular Layer of the Cerebellum

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Coding in the Granular Layer of the

Cerebellum

Progress in Brain Research

Issue Editor: M.A.L. Nicolelis

E. De Schutter1 and J.G. Bjaalie2

1. Born-Bunge Foundation, University of Antwerp, Universiteitsplein 1,

B2610 Antwerp, Belgium, Fax +32-3-8202669

2. Department of Anatomy, Institute of Basic Medical Sciences, University of

Oslo, P.O.Box 1105 Blindern, N-0317 Oslo, Norway

AbstractIn this paper we formulate a new theory of how information is coded along

the parallel fibers in the cerebellar cortex. A question which may arise is why

such a new theory is needed at all. Previously we have argued that the

dominant theory of cerebellar coding, i.e. the perceptron learning theory

formulated by Marr (1969) and Albus (1971) that was extended by Ito (1982;

1984) and more recently by Mauk and colleagues (Raymond et al., 1996;

Mauk, 1997), does not comply with current experimental data. The basicassumption of these theories, that long-term depression (LTD) is the

mechanism by which memory traces are coded at the parallel fiber to

Purkinje cell synapse and that LTD induction is controlled by the climbing

fiber input, is not beyond doubt (De Schutter, 1995; 1997). For example,

recent data showing that LTD can be induced by pure parallel fiber excitation

without any conjunctive signal (Hartell, 1996; Eilers et al., 1997; Finch and

Augustine, 1998) does not conform to the theory proposed by Marr, Albus

and Ito. Instead these findings indicate that the climbing fiber signal is not

required to induce learning at the parallel fiber synapse and that, in fact, LTD

may have quite a different function. Moreover, studies using transgenic mice

in which LTD induction was blocked have raised serious doubts about a link

between LTD and cerebellar motor control (e.g. De Zeeuw et al., 1998) and

about the necessity of cerebellar LTD for eyeblink reflex conditioning

(reviewed in De Schutter and Maex, 1996). As we have discussed this issue

extensively elsewhere (De Schutter, 1995; De Schutter and Maex, 1996; De

Schutter, 1997), we will not further address it here.Instead we will focus on the function of the input layer of the cerebellar

cortex, the granular layer, and the mossy fiber projections to it. As this layer

processes the mossy fiber input it makes sense to first try to understand how

it transforms inputs to the cerebellum into parallel fiber signals before

considering in more detail the role of LTD at the parallel fiber synapse. Such

a study is necessary, especially now that recent experimental data have

raised doubts about the effectiveness of parallel fiber input in exciting

Purkinje cells (Cohen and Yarom, 1998; Gundappa-Sulur et al., 1999).

Most of the data presented and reasoning developed in this chapter concern

the hemispheres of the rat cerebellum and the corticopontine

somatosensory projections to this region. This emphasis reflects both our

own work and the wealth of data available on these parts of the cerebellum.

Considering the conserved cytoarchitecture from archi- to neocerebellum

(Palay and Chan-Palay, 1974; Ito, 1984) it seems reasonable to expect that

our conclusions about the neocerebellum will also apply to the rest of thecerebellum.

A short review of the anatomy and physiology of the

granular layer

In this section we briefly introduce the reader to both well known facts and

more recent data on the granular layer of the cerebellar cortex. As mentioned

before we focus on the mossy fiber system which is numerically the most

important input to the cerebellum (Murphy and Sabah, 1971; Brodal and

Bjaalie, 1992). For the processing of mossy fiber input the anatomy of

cerebellar cortex can be approximated by a two-layered network. The granule

cell input layer encodes the incoming mossy fiber signals and transmits

them through the parallel fiber system to the output layer, consisting mainly

of the Purkinje cells. In both layers neural activity is controlled by inhibitory

neurons, the Golgi cells in the input layer, and the basket and stellate cells inthe output layer.

Because of the large number of granule cells (about 101 billion in man;


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Andersen et al., 1992), the granule cell to Golgi cell ratio is very high. Recent

estimates of a ratio of 400 (Korbo et al., 1993) are lower than those used

previously (Ito, 1984), but all these studies have probably underestimated

the ratio as they assumed that all large neurons in the granular layer are

Golgi cells which is not the case (Dieudonn and Dumoulin, 2000; Geurts et

al., 2000). Mossy fibers activate both the excitatory granule cells and the

inhibitory Golgi cells in the granular layer (Fig. 1).

Figure 1

Schematic representation of the organization of the granular layer of the cerebellum,

transverse view. Mossy fibers originating external to the cerebellum excite both granule

and Golgi cells, granule cells excite by their long parallel fibers Golgi cells, and Golgi

cells inhibit granule cells. Each granule cell receives about 4 mossy fiber inputs and

about 10 inhibitory contacts but it is unclear whether these come from different Golgi

cells or not. The number of parallel fiber contacts onto Golgi cells is not known.

Each granule cell receives input from multiple mossy fibers, but

physiological recordings suggest that mossy fibers projecting to a particular

region code similar information (see below and Bower et al., 1981). The

granule cell axon has an ascending part (Gundappa-Sulur et al., 1999) whichmay have a strong excitatory influence on overlying Purkinje cells (Bower

and Woolston, 1983; Cohen and Yarom, 1998) and then splits into two

parallel fiber segments. The parallel fibers do not only transmit information to

the Purkinje cell output layer, but also provide additional excitatory input to

Golgi cells. Each Golgi cell in turn inhibits the many granule cells present

within the range of its axonal arbor (Eccles et al., 1966). Unique to the

granular layer circuit is the absence of inhibitory connections between Golgi

cells and of excitatory connections between granule cells. Combined with

the parallel fiber excitation of Golgi cells and their inhibition of granule cells,

this means that it contains pure feedback inhibition loops. In addition the

direct excitation of Golgi cells by mossy fibers forms a feed-forward

inhibition connection.

Recently cerebellar slice recordings have provided additional insights in

granule and Golgi cell physiology. Granule cells are regularly firing neurons

which do not show adaptation (D'Angelo et al. 1995; Brickley et al. 1996). Inrat cerebellar slices they have a rather high threshold, requiring co-activation

of two or more mossy fiber inputs to fire the cell (D'Angelo et al. 1995). The

mossy fiber to granule cell synapse can undergo long-term potentiation

(LTP; D'Angelo et al., 1999) and under particular conditions granule cells

may show burst firing (D'Angelo et al., 1998).

Golgi cells are spontaneously active in slice (3-5 Hz; Dieudonn, 1998) and

show firing rate adaptation upon current injection. This firing rate adaptation

plays an important role in how these cells synchronize in vivo (see below and

Maex et al., 2000).

The fractured somatotopy of mossy fiber projectionsThe response characteristics of the granular layer to tactile stimulation have

been studied extensively in the cerebellar hemispheres of the anesthetized

rat. At the level of field potentials which probably reflect the activation of

mossy fiber synapses, one finds a fractured somatotopy of the tactile

receptive fields (Shambes et al., 1978; Welker, 1987; Bower and Kassel,

1990). This means that the receptive field map is a mosaic of small patches


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(on the order of a few 100 _m diameter), each representing a different part of

the body surface (Fig. 2).

Figure 2

The tactile receptive field map of the cerebellar folia crusIIa, crusIIb, and the paramedian

lobule (PML). Each patch represents either ipsilateral, contralateral or bilateral responses.

The patch-like mosaic representation of different body parts, with adjacent patches

often receiving projections from non-adjacent body parts, has been termed fractured

somatotopy. The schematic map shown in this figure emphasizes the multiple

representations of the upper lip. Modified from Welker (1987) and Bower and Kassel

(1990).

Furthermore, each particular input location, e.g. the upper lip region, is

represented multiple times, but always surrounded by different neighboring

patches. This particular arrangement of the receptive fields, combined with

the dominance of the ascending component of the granule cell axon (Bower

and Woolston, 1983; Gundappa-Sulur et al., 1999), has led Bower (1997) to

propose that the parallel fibers may have a role different from the ascending

component. The parallel fiber would carry context signals from distant

patches to the Purkinje cells which integrate these signals with the dominant

local mossy fiber input from the underlying patch.The field potentials recorded in each of the patches in response to tactile

stimulation contain two components. The early one (8-10 ms delay) is

caused by a direct pathway from the trigeminal nuclei, while the late one

(16-22 ms delay) reflects mossy fiber activation through a thalamo-cortico-

ponto-cerebellar loop (Morissette and Bower, 1996). The two separate

mossy fiber pathways project to the same patches in cerebellar cortex (Bower

et al., 1981), though the pontocerebellar mossy fibers tend to have a more

diffuse projection and carry more often bilateral signals than the trigeminal

ones (Morissette and Bower, 1996).

Recently we have started recording the responses of inhibitory Golgi cells in

these areas to tactile stimulation (Fig. 3) (Vos et al., 1999b; 2000).

Figure 3

Response of two Golgi cells to tactile stimulation. A: Recording sites in crus II marked

on top view of the cerebellum. B: Same on a transverse section. C: Location of the

tactile stimulus. D: Responses of the two cells, in both cases the complete response


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over 600 ms following the stimulus (notice the long silent period) and a blow up of the

initial response (first 50 ms) are shown. Because of the double early peak (7 and 11

ms) the cell to the left is presumed to receive direct trigeminal mossy fiber input, the

one to the right is activated through parallel fiber synapses. Both cells show an early

trigeminal (< 15 ms) and late corticopontine component. Modified from Vos et al.

(1999b).

In contrast to the fractured somatotopy observed in field potentialrecordings, Golgi cell receptive fields are very large and often bilateral. They

usually also reflect the consecutive activation of the two different mossy

fiber pathways, with delays of the respective peak responses which are

similar to those observed in the field potential recordings. The large receptive

fields observed in Golgi cell recordings are probably due to the activation of

each Golgi cell by parallel fibers originating from patches with different input

representations. In addition, for most Golgi cells it is possible to find a

particular response pattern which has a trigeminal component consisting of

two or more sharp and highly accurate peaks (Fig. 3). This specific response

pattern can be evoked from only one location on the rat's face and

presumably reflects the direct activation of the Golgi cell by mossy fibers in

the local patch (Vos et al., 1999b; 2000).

Another intriguing property of the Golgi cell responses is the long silent

period following the initial excitatory response (Fig. 3; Vos et al., 1999b; De

Schutter et al., 2000). As Golgi cells are spontaneously active this silent

period is quite noticeable. Similar silent periods are also found in other partsof the somatosensory system (Mountcastle et al., 1957; Mihailoff et al.,

1992; Nicolelis and Chapin, 1994), where they are assumed to be the

consequence of local feedforward inhibition (Dykes et al., 1984). Note,

however, that in somatosensory cortex such silent periods are observed in

excitatory neurons while inhibitory neurons remain active (Brumberg et al.,

1996). This is clearly not the case in the granular layer where a silent period

is observed in the inhibitory Golgi cell.

Coding in the corticopontine pathwayKnowing the properties of the corticopontine pathway is important as this

may provide clues to what type of information the cerebellum wants to

receive. Compared to the situation in the cerebellar hemispheres the

mapping from the neocortex to the pontine nuclei (PN) is relatively simple. In

the developing rat, axons originating in restricted cortical regions grow into

widespread but specific lamellar subspaces in the PN (Leergaard et al., 1995,

Fig. 4A).


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Figure 4

The orderly topographic mapping of the cerebral cortex onto the pontine nuclei in

developing and adult rats. A: Projections in the developing rat. Sagittal clip plane, 200

_m thick, from a 3-D computerized reconstruction of the PN. Rostral is upwards and

ventral to the left. Data from multiple single-tracing experiments (injection sites shown

on inset drawing of the cerebral hemisphere) are superimposed in one model. Dots

represent the distribution of labelled axons in the PN. A shift in cortical site of origin (red

- yellow - blue) corresponds to an internal-to-external shift of distribution in the PN,largely preserving neighbouring relationships. B: Adult rat projections from three major

adjacent SI body representations. Presentation as in A. Note that the representations of

the trunk (yellow) and hindlimb (blue) surround the representation of the face (red). The

adult PN contains multiple representations for each body parts, but overall

neighbouring relationships of the SI map are preserved. C: Cartoon of the Leergaard et

al. (1995) hypothesis explaining the establishment of general topographic organisation

in the rat corticopontine system. Temporal gradients, from early to late, are illustrated by

the colours red-yellow-blue. Early arriving corticopontine fibres innervate the early

established central core of the PN, whereas later arriving fibres innervate progressively

more external volumes. (A) and (C) are modified from Leergaard et al. (1995) and (B)

from Leergaard et al. (2000).

There is an orderly topographic relationship between cortical sites of origin

and the PN lamellar target regions, possibly related to temporal gradients

operative within the cortex and PN (Fig. 4C). The anterolateral part of the

cortex projects to an internal, central core of the PN, ventral to thedescending fiber tract. Cortical sites at increasing distance from this

anterolateral region innervate progressively more external lamellar

subvolumes. This 3-D pontine topographical arrangement observed in

young animals preserves the overall neighboring relationships of the cortical

map.

Corticopontine projections in adult animals have classically been described

as topographically organized (for review, see Brodal and Bjaalie, 1992).

Compared to the initially widespread projections in the young animal, adult

projections are more restricted and the continuous lamellar pattern is broken

into pieces, described as patches or clusters within lamellar regions (Bjaalie

et al., 1997; Leergaard and Bjaalie, 1998, Leergaard et al., 2000a). In single

sections these separated patches may be interpreted as the substrate for the

fractured map in cerebellar cortex. But, as neighbor relationships among the

multiple patches or clusters of terminal fields in the PN largely reproduce

those found in the neocortex (Leergaard and Bjaalie, 1998; Leergaard et al.,2000a), the overall mapping of the cortex onto the PN is primarily

continuous, and not fractured. An example is shown in Figure 4B. With the

use of anterograde axonal tracing, a sequence of electrophysiologically

defined cortical primary somatosensory (SI) body representations (face -

trunk - hindlimb) is here seen to project onto the PN in an orderly inside-out

fashion. The face projection occupies a central core region of the PN,

whereas the projection from the adjacent trunk representation surrounds

this central core. The SI hindlimb projection is located further away, in a

more external location of the PN. There is no mixing of the projections from

these SI body representations in the pontine map. What then happens at a

smaller scale? For example, could there be a fractured projection from

smaller regions of SI onto the PN? We are currently studying the detailed

organization of the projection from the SI face area with double anterograde

tracing from individual whisker barrels and 3-D computerized reconstruction

(Leergaard et al., 2000b). Again, we observe a primarily organized projection

pattern.

Furthermore, we have started recording the responses in the PN to

peripheral stimulation (Eycken et al., 2000). When the recording electrode is

advanced in steps of a few micrometers through the PN, locations of tactile

receptive fields change gradually. We have so far not observed any abrupt

transitions or major jumps from one body region to another, as would be

expected from a fractured map.

While the mapping of the neocortex onto the PN may be relatively simple in

terms of cartography, it becomes more complicated if one considers one of

the stimulus attributes being transmitted, i.e. the representation of different

receptive fields. This issue has been studied in the somatosensory and the

visual system. Thus, the projection from SI cortex to PN contains a more

even distribution of distal versus proximal body representations than SI

itself (verby et al., 1989; Vassb et al., 1999). Similarly, the corticopontine

projection from several visual cortical areas has a more even distribution of

foveal versus extrafoveal representations than the neocortex (Bjaalie andBrodal, 1983; Bjaalie, 1985, 1986).

It is known that distal body parts are emphasized in the somatosensory


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cortical areas, in the sense that they occupy disproportionally larger cortical

volumes (Nelson et al., 1980). If this emphasis were maintained in the

pathway from somatosensory areas to the cerebellum, one would expect

even densities of corticopontine neurons within each somatosensory area.

With the use of retrograde axonal tracing and cortical map reconstruction,

we have found uneven densities of corticopontine neurons in SI of the cat

(verby et al., 1989) and SI (area 3b) and areas 1 and 2 of the monkey

(Vassb et al., 1999). In these areas and species, the body parts with thelargest cortical magnification factors always contain the lowest densities of

corticopontine neurons. Figure 5 exemplifies this principle in monkey area

3b.

Figure 5

Flattened map of the cynomolgus monkey area 3b, showing density gradients of

corticopontine cells in shades of grey. White indicates high density; dark grey low

density. The PN was injected with large amounts of wheat germ agglutinin horseradish

peroxidase and the retrogradely labelled neurons in the cortex were quantitatively

mapped. A: Three-dimensional landscape presentation of the density distribution. B:

Two-dimensional density map. Dashed lines indicate the approximate boundaries of

the major body representations in area 3b, as outlined by Nelson et al., (1980). Note

that the highest densities of corticopontine neurons are found in the representations of

the trunk, proximal hindlimb (HL), and proximal forelimb (FL). The same pattern is

found in other postcentral somatosensory areas. Modified from Vassb et al. (1999).

It can be seen that regions representing the trunk and proximal limbs contain

higher densities of corticopontine neurons than regions representing distal

limbs. The lower densities are particularly evident in the distal forelimb

representation. Thus, the distal forelimb representation, which is known to

be strongly emphasized in terms of cortical volume, appears to be de-

emphasized in the corticopontine projection, or not emphasized to the same

extent as in the cortex.

The distribution of corticopontine neurons in visual areas of the cat followsthe same principles. Similar cortical map reconstructions (Bjaalie and Brodal,

1983; Bjaalie, 1985, 1986) show that regions representing the central visual

field (analogous to distal forelimb) contain lower densities of corticopontine

neurons than regions representing the peripheral visual field (analogous to

proximal body regions). But in terms of the number of corticopontine

neurons devoted to equally sized visual field blocks, central vision was still

moderately over-represented compared to peripheral vision (due to high

cortical magnification factors for central vision). Fig. 6 shows corticopontine

density distribution in the cat visual area 18.


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Figure 6

Distribution of corticopontine neurons in cat visual area 18. The PN was injected with

large amounts of wheat germ agglutinin horseradish peroxidase and the retrogradely

labelled neurons in the cortex were quantitatively mapped. The histograms shows the

distribution of corticopontine neurons in equally sized blocks of the lower visual field

close to the vertical meridian (azimuth 0( - 20(). Upper left: Densities of corticopontineneurons (cells/mm2 cortex) decrease from the representation of the lower peripheral

visual field (elevation -50() to the central visual field representation (elevation 0(). Lower

left: The number of corticopontine neurons devoted to each equally sized block of the

visual field (cells/mm2 cortex x mm2 cortex/visual field block) is higher for blocks close

to the central visual field representation. The perimeter chart shows the relative strength

of the corticopontine projection from different parts of the visual field represented in

area 18, based on quantitative data exemplified in the lower right histogram. Modified

from Bjaalie (1985).

The findings summarized in Figs. 5 and 6 have important implications as

they suggest that cortical information is rescaled and partially renormalized

before being transmitted to the cerebellum. While maps in the cortex

typically overrepresent functionally important parts of the input map, like the

fovea for the visual system, the hand for the monkey somatosensory system

or the vibrissae for the rat somatosensory system, this may not be the case

to the same extent for input to the cerebellum. As far as the map of

somatosensory projections to the rat cerebellar hemisphere is known (one

should realize that only the crowns of the folia have been mapped in detail,

e.g. Fig. 2) it seems that vibrissal input is represented to a smaller extent

than in somatosensory cortex (Chapin and Lin, 1990; Voogd and Glickstein,

1998).

We can conclude that the corticopontine projections transmit another

subset of the input space than is represented in the cerebral cortex.

Furthermore, it seems likely that the transformation from a continuous map

in SI to a fractured somatotopic map in the cerebellum takes place primarily

in the pontocerebellar projection given that the corticopontine projection is

not basically fractured, but the pontocerebellar pathway needs further study.

Finally, it is well known that the corticopontine projections are among the

fastest pathways in the human nervous system (Allen and Tsukahara, 1974).

The function of the cerebellar granular layer

Most cerebellar theories give little consideration to the function of the

granular layer; they focus instead on the interaction between parallel fibers

and Purkinje cells (Ito, 1982; Braitenberg et al., 1997) and, more recently,

also on that between Purkinje cells and neurons in the deep cerebellar nuclei

(Raymond et al., 1996). This focus on the output side of the cerebellar

circuitry may be misconceived, considering that the granular layer contains

98% of the cerebellar neurons (Palay and Chan-Palay, 1974). In fact, Marr

(1969) and Albus (1971) did consider the function of the granular layer in

detail in their original papers. They contribute it an important function in

recoding the mossy fiber input so that the simple perceptron learning rule,

which they propose for the parallel fiber to Purkinje cell synapse, can be

applied to complex input patterns. Without such a recoding scheme

perceptrons cannot learn to distinguish patterns that are not linearly

separable (Minsky and Papert, 1969). Albus' paper contains a nice examplewhere he shows how the recoding of mossy fiber input by the granular layer,

which is in effect a combinatorial expansion by about two orders of


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magnitude, can circumvent this problem. In these theories the inhibitory

Golgi cells control the activation threshold of granule cells, thereby keeping

the number of active parallel fibers relatively small and constant over large

variations in the number of active mossy fibers (Marr, 1969). This control

over the number of active parallel fibers enhances the performance of the

perceptron learning rule. Albus (1971) used the word "automatic gain

control" to describe the role of the feedback inhibition by Golgi cells. Overall

this would restrain the number of active parallel fibers contacting a singlePurkinje cell to 1 % (Albus, 1971) or 0.3 to 6 % (Marr, 1969).

We have recently criticized the proposed gain control function of Golgi cells

(De Schutter et al., 2000) and will not repeat our arguments in detail here.

Instead we will focus on our recent modeling and experimental work, which

suggests another function for cerebellar Golgi cells: the control over the

timing of granule cell spikes (Maex and De Schutter, 1998; Vos et al., 1999a).

Golgi cells fire synchronously along the parallel fiber beam Our modeling

studies of cerebellar cortex indicate that the cerebellar granular layer is

highly prone to synchronous oscillations (Maex and De Schutter, 1998b). A

typical example is shown in Fig. 7.

Figure 7

Raster plot showing spike timing of 10 Golgi cells (upper part) and 300 granule cells

(lower part). Initially the network is not activated and only the Golgi cells fire

occasionally. At the time indicated by the vertical line homogeneous 40 Hz mossy fiber

input is applied and the complete circuit starts firing synchronously at a regular rhythm

of about 20 Hz. Simulation of the standard network configuration described in Maex

and De Schutter (1998b) but with a more dense packing of the units (30 Golgi cells,

21555 granule cells and 2160 mossy fibers).

The raster plots show the activity in a large one-dimensional network

simulation, where all units are positioned along the parallel fiber axis.

Initially, no mossy fiber input is provided and the spontaneous activity ofGolgi cells results in a low rate of desynchronized firing. When the simulated

mossy fibers are activated, however, all Golgi cells synchronize immediately

and start firing rhythmically. In comparison, the granule cells show more

complicated behavior. While they are also entrained in the synchronous

oscillation, they fire less precisely and often skip cycles. The differences in

behavior of individual granule cells in Fig. 7 can be explained by the

randomization of connectivity and intrinsic excitability parameters (Maex and

De Schutter, 1998b), indicating that such relative small sources of variability

can generate complex activity patterns within the overall regular oscillation.

The appearance of synchronous oscillations is explained by the intrinsic

dynamics of the pure feedback inhibition circuit (Fig. 1). This can be easily

understood by first considering the subcircuit consisting of a single Golgi

cell and its many postsynaptic granule cells. Inhibitory neurons exert a

strong influence on the timing of action potentials in their target neurons

(Lytton and Sejnowski, 1991; Cobb et al., 1995). The simulated granule cells

will fire when inhibition is at its lowest, which is just before the next Golgi

cell spike. Consequently the large population of granule cells postsynaptic

to one Golgi cell will fire at about the same time. The loosely synchronous


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granule cell activity then excites the same Golgi cell and causes it to fire

immediately, leading to the establishment of a synchronized oscillation

within this subcircuit, with granule spikes shortly preceding the Golgi cell

spike. The long parallel fibers which are typical for the structure of the

cerebellar cortex couple many of these oscillatory subcircuits together.

Common parallel fiber input will cause Golgi and granule cells located along

the same transverse axis to fire (almost) synchronously.

This is a dynamic property of the cerebellar circuitry; once the granular layeris activated sufficiently the most stable form of spiking is a synchronous

oscillation (Maex and De Schutter, 1998b). The accuracy of this

synchronization increases with increased mossy fiber activity, which also

leads to an increased Golgi cell firing rate (Maex and De Schutter, 1998b).

Consequently we expect to find a firing-rate dependency of the

synchronization (Maex et al., 2000). As seen in Fig. 7 the synchronization is

immediate upon activation; there is no delay due to the slow parallel fiber

conduction velocity (Maex and De Schutter, 1999). Finally, Golgi and granule

cell populations are synchronized over the complete extent of the transverse

axis where mossy fibers are activated, even if this is much longer than the

mean parallel fiber length of 4.7 mm (Pichitpornchai et al., 1994). Because

both cell populations fire in loose synchrony Golgi cell activity can be used

to estimate the timing of granule cell spikes, though individual granule cells

may skip cycles of the oscillation (Fig. 7). This is important as one cannot

isolate single granule cells in vivo, while it is relatively easy to isolate Golgi

cells (Edgley and Lidierth, 1987; Van Kan et al., 1993).These modeling predictions were confirmed using multi-single-unit

recordings of spontaneous Golgi cell activity in the rat cerebellar

hemispheres (Vos et al., 1999a). A total of 42 Golgi cell pairs in 38 ketamine-

xylazine anesthetized rats were recorded. Of these, 26 pairs were positioned

along the transverse axis (i.e. along the same parallel fiber beam), while the

other 16 pairs were located along the sagittal axis (no common parallel fiber

input). All transverse pairs except one showed a highly significant coherence

measured as the height of the central peak in the normalized cross-

correlogram. An example of such a cross-correlogram obtained from a pair

of Golgi cells along the transverse axis is shown in Fig. 8.

Figure 8

Cross-correlation of spontaneous activity of two Golgi cells receiving common parallel

fiber input. The highly significant central peak (the cross-correlogram has been

normalized for firing frequency) is indicative of synchronous firing which is not very

accurate as the peak is wide. This is the same Golgi cell pair as of Fig. 4. See Vos et al.

(1999a) for experimental and statistical procedures.

Conversely, in 12 out of 16 sagittal pairs no synchrony could be found. The

remaining four sagittal pairs showed low levels of coherence, but in each of

these pairs the Golgi cells were located within 200 _m from each other. We

assume that in these latter four pairs the cells were so close to each other

that their dendritic trees overlapped (Dieudonn, 1998), allowing them to

sample common mossy and/or parallel fiber input despite their parasagittal

separation.

These findings confirmed the main prediction of the network simulations:

Golgi cells along the parallel fiber beam fire indeed synchronously.

Additionally, as predicted, the accuracy of synchronization, evidenced by

higher and sharper central peaks in the cross-correlogram, increased with

the Golgi cell firing rate (Fig. 1 of Vos et al., 1999a). This indicates that

synchronization may be much more accurate in awake animals, compared to

the loose synchrony observed in the anesthetized rat. The only data

presently available from awake animals are field potential recordings (Pellerin


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and Lamarre, 1997; Hartmann and Bower, 1998). These studies have also

demonstrated the presence of oscillations in the granular layer that may

correspond to those predicted by the model.

The effect of spatially localized mossy fiber input

In the previous section we considered the synchronization of Golgi cells in

response to a spatially homogeneous mossy fiber input in the networksimulations and compared this to experimental data obtained without any

stimulation. This is of course a rather artificial assumption. Considering the

patchy receptive fields in the granular layer (Fig. 2) one expects stimulation

to cause spatially heterogeneous mossy fiber activation.

Recent modeling work in our laboratory demonstrates that a similar behavior

can be observed when a patchy mossy fiber input is applied. Specifically, if

two patches are activated by comparable levels of mossy fiber input they will

synchronize immediately, even if separated by a few millimeters of only lowly

activated granular layer (Franck et al., 2000). This can be observed in Fig. 9A,

which shows the spike trains of the model Golgi cells and of a subset of

granule cells in a one-dimensional model with strong feedback inhibition.

Activation of two small patches (200 _m diameter containing about 50

mossy fibers and 500 granule cells each, 1 mm separation) leads to the

immediate synchronization of all Golgi cells along about 6 mm of the parallel

fiber beam overlying the patches. As parallel fibers are 5 mm long in thenetwork model, this means that all Golgi cells receiving input from the two

patches become entrained in the rhythm, though the synchronization is

clearly less robust than that evoked by homogeneous input (Fig .7). The

other Golgi cells in the network fire less than before or are hardly affected at

all.

The picture looks somewhat different for granule cells. In Fig 9 only a small

subset of granule cell traces can be shown, so the borders of the patches are

not represented. It can nevertheless be seen that they are activated inside the

patches only. Between the two patches and at the outer borders of the

patches they are actively inhibited by the activated Golgi cells. The granule

cell activity within and between the two patches is highly synchronized. Like

for the fully activated network (Fig. 7) granule cells spike together with Golgi

cells, but sometimes skip cycles.


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Figure 9

Comparison of firing patterns and parallel fiber activity in a network with strong

feedback inhibition (A,C) and a network with strong feed-forward inhibition (B, D). A, B:

Firing activity in all Golgi cells and a selection of granule cells. Initially the network is

slightly activated by diffuse mossy fiber input (mean rate 5 Hz in A and 10 Hz in B). At

the time indicated by the blue line two patches of 200 _m diameter, separated by 1mm, are activated (40 Hz mossy fiber input in A, 80 Hz in B). Spike trains from neurons

in the patches are colored red and green. Because a random selection of granule cell


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spike trains is shown their spatial position does not have a direct correspondence to

that of the Golgi cells. C, D: Conduction of waves of spike activation along parallel

fibers. The left and right panels shown are separated in time by 4 ms. Random

sampling of parallel fibers originating within and outside the two patches. Spikes

colored following patch of origin. See text for more details. In A, C GPF-AMPA is 80 nS

and GGABA 50 nS; in B,D MF(GoC connection probability is 0.2 and GMF-AMPA 30

nS and GPF-AMPA is 4 nS, other parameters as in standard network configuration

described in Maex and De Schutter (1998b) but with more dense packing of cells (seeFig. 7).

In addition granule cells sometimes fire bursts of two spikes. The latter

behavior was even more pronounced when the network parameters from

previous studies (Maex and De Schutter, 1998b) were used (to diminish

bursting in Fig. 9A the synaptic strengths of parallel fiber and Golgi cell

synapses have been raised, making the feedback inhibition loop stronger).

The possible importance of granule cell bursting for induction of synaptic

plasticity at the parallel fiber to Purkinje cell synapse (Linden and Connor,

1995; Finch and Augustine, 1998) has been discussed previously (De

Schutter et al., 2000). It is interesting to note that bursting behavior is easier

to evoke with spatially localized activation. At present we are evaluating the

bursting behavior of the model further by introducing more accurate

descriptions of the granule cell excitability (D'Angelo et al., 1998) into the

network simulations.

In conclusion, the simulation of Fig. 9A demonstrates that, in a networkmodel with strong feedback inhibition, activation of spatially separated

patches can also couple the activity of Golgi cells. In their effect on granule

cell firing Golgi cells seem to have both a discriminating and an integrating

function: they increase the contrast in firing rate between activated and non-

activated granule cells and they synchronize firing of activated granule cells.

In contrast, if a similar input is applied to a network version with weak

feedback inhibition and strong feed-forward inhibition the situation looks

quite different (Fig. 9B). These networks show no synchronization of Golgi

cell firing for homogenous mossy fiber input (Maex and De Schutter, 1998b).

In Fig. 9B the Golgi cells are more active because of their direct excitation by

mossy fibers. Only the Golgi cells receiving increased mossy fiber input in

the patches (and a few of their immediate neighbors) show a response to the

activation: they increase their firing rate without synchronizing. The granule

cell activity is very heterogeneous: some fire at rates similar to those in 9A,

others do not. While some of these spikes are clearly synchronized within apatch, there is almost no synchronization of activity between the two

patches. The synchronization within patches is explained by common

inhibition from one Golgi cell. As the parallel fiber activation of Golgi cells is

very weak in these simulations, it is not sufficient to synchronize the Golgi

cells.

Spatio-temporal coding along the parallel fiber beam

In the left panels of Fig. 9 we compare the granule cell spiking in a

synchronized version (Fig. 9A) and desynchronized version (Fig. 9B) of the

granular layer network model. In the right panels we compare the effect of

synchronization on parallel fiber spike transmission by showing two

snapshots for each network version.

Both simulations show waves of spikes traveling along the parallel fiber

beam, but with an important distinction. In the feedback inhibition model thepatches fire loosely synchronized so that the spikes originate in both

patches, while in the feed-forward inhibition model all the spikes that can be

observed at one time originate in only one of the patches. Only rarely did one

observe spikes originating outside the patches or, in the case of Fig. 9D, a

spike originating in the other patch. The comparison of these two

simulations suggests that at the low firing rates present in the model granule

cells the synchronization of the feedback inhibition model has an important

effect on the patterns of parallel fiber spiking that are perceived by Purkinje

cells. In particular, in the synchronized model the two patches activate

Purkinje cells at roughly the same time (Fig. 9C) while without

synchronization they will do so separately (Fig. 9D).

The spike waves of Fig. 9C-D are reminiscent of the tidal waves proposed by

Braitenberg et al. (1997), with the important difference that their timing is

generated inside the cerebellar cortex, not outside of it. But Braitenberg et al.

(1997) proposed that only where all the spikes synchronize along the parallel

fiber beam Purkinje cells would be activated. Because of the loose

synchronization in the network model this is unlikely to occur. We assume

that accurate synchronization may not be important, at least not along the


13/18

parallel fiber beam, because our Purkinje cell model (De Schutter and Bower,

1994a,b) is a very poor coincidence detector (De Schutter, 1998). This is to

be expected as the Purkinje cell dendrite does not contain fast sodium

channels (Stuart and Husser, 1994). Instead its window of temporal

integration is determined by much slower activating dendritic calcium

channels (Regan, 1991; Usowicz et al., 1992).

There are two ways in which the synchronized spike waves may be decoded

by Purkinje cells. The most simple one is to assume a population rate codingscheme (Rieke et al., 1997). Because both patches fire loosely synchronized

(Fig. 9A) they cause short bursts of spiking activity along the parallel fiber

beam (Fig. 9C) during their activation. Purkinje cells receiving synaptic input

from those parallel fibers could simply integrate this input with a total

excitation determined by the size and number of patches activated (for a

particular mossy fiber input rate). Supportive for this hypothesis is that the

conduction time needed for a spike to travel along one half of a parallel fiber

(5-12 ms; Bernard and Axelrad, 1991; Vranesic et al., 1994) is in the same

time range as the typical time window within which granule cells in both

patches spike in the simulations of Fig. 9A (about 10 ms).

An alternative hypothesis is to assume a temporal code, captured in the

relative timing of the granule cell spikes. It was Hopfield (1995) who first

hypothesized that the nervous system can use relative phase lags between

spikes to encode information. In the context of pattern recognition such a

temporal code has the advantage of being much less sensitive to stimulus

amplitude than standard rate codes (which are used by the perceptronlearning rule of Marr and Albus). While Hopfield proposed that coincidence

detection combined with different afferent delays would be used to decode

such phase lags, one can imagine alternative schemes which decode the

phase lags directly (Steuber and Willshaw, 1999).

Whichever hypothesis one prefers, the synchronization of firing of granule

cells which are positioned along the same parallel fiber beam contributes to

the transformation of spatial patterns present in the mossy fiber input into a

temporal pattern that is transmitted along the parallel fiber system.

According to the population rate coding hypothesis it is the burst of

synchronized spikes which associates the activity originating in two spatial

locations; in the temporal coding the actual phase lags between spikes is the

source of information. To distinguish between these two possibilities it

would be helpful to know how accurate the timing is in awake animals, as

the temporal coding hypothesis requires more accurate synchronization

than that observed in anesthetized rats (Vos et al., 1999a; Maex et al., 2000).We are currently investigating this issue (Vos et al., 1999c).

Bringing it all together

Pontine sensory input to the cerebellum copies cortical activity, without any

obvious mixing of signals. Furthermore, the output from the SI cortex to the

cerebellum via the pontine nuclei is renormalized to represent different body

parts more equally (Figs. 5-6). Because of the patchy, fractured somatotopy

of mossy fiber input (Fig. 2), tactile input will generate specific spatial

patterns consisting of several co-activated patches in the granular layer (see

also Peeters et al., 1999). The complex spatial pattern of activation of

patches may therefore be used to distinguish between different stimuli and/

or activation patterns in neocortex. We propose that the Golgi cell feedback

inhibition loosely synchronizes the activity of granule cells in co-activated

patches and thereby supports the transformation of a spatially encodedmossy fiber signal into a temporal code of spike waves transmitted along the

same parallel fiber beam. Without synchronization much higher granule cell

firing rates are required to ensure loose coincidence of spikes originating in

different patches (e.g. Fig. 9D).

The spatio-temporal transformation hypothesis accords with the properties

of the synchronization described above. The immediate synchronization of

Golgi cells (Fig. 7) allows for an efficient transformation, while the lack of

accuracy fits with the variable conduction velocities of parallel fibers (Bernard

and Axelrad, 1991; Vranesic et al., 1994) which will slowly desynchronize the

signal anyway. We expect that in awake animals transient synchronous

oscillations linking several different or identical receptive field patches rise

and wane continuously, transforming the spatial pattern of input into short

sequences of synchronous spike waves along the parallel fiber beam. The

amplitude of the input pattern will determine the frequency of these

oscillations (Maex and De Schutter, 1998b).

In principle this spatio-temporal code hypothesis is compatible with an

additional combinatorial expansion of the mossy fiber signal, as suggested

by Marr (1969) and Albus (1971). Nevertheless, alternative explanations for


14/18

the large number of granule cells are available. Our modeling studies show

that a minimum number of parallel fiber contacts onto each Golgi cell must

be activated to sustain the synchronous oscillations (Maex and De Schutter,

1998a). This is much more easily achieved in a sparsely activated network

containing many granule cells.

In support of the spatio-temporal code hypothesis we have found that the

most important stimulus aspect determining the fine temporal shape of

Golgi cell responses is the part of the receptive field being activated, whilestimulus amplitude has little or no effect (Volny-Luraghi et al., 1999; Vos et

al., 1999b). In other words, the granular layer cares about the spatial pattern

of mossy fiber input, which is determined by the stimulus location, not about

stimulus amplitude. The renormalization of space in the corticopontine

projection (Figs 5-6) also confirms the importance of spatial relations in this

system.

Several questions remain. How do Purkinje cells decode these spike waves

and what do the pontine nuclei contribute to this proposed scheme? At the

level of the Purkinje cell many mechanisms are possible. The population rate

coding scheme is compatible with the perceptron learning as proposed by

Marr (1969) and Albus (1971), with the important addition of a spatio-

temporal recoding not included in their theories. The phase coding scheme

may require more specific learning rules (e.g. Steuber and Willshaw, 1999) or

interactions between parallel fiber excitation and inhibition by stellate and

basket cells (Jaeger et al., 1997; Jaeger and Bower, 1999).

Concerning the pontine nuclei an additional intriguing possibility is thatthey enhance the generation of synchronous oscillations in the granular

layer. The synchronization of Golgi and granule cell spiking between patches

assumes that the mossy fiber excitation of each patch is roughly equal

(Franck et al., 2000). Therefore it would be useful to have a mechanism

available which keeps mossy fiber excitation evenly distributed across

activated fibers. How the pontine nuclei could achieve this with only very few

interneurons (Brodal et al., 1988; Border and Mihailoff, 1990) remains

unclear, though subcortical projections to the pontine nuclei (reviewed in

Brodal and Bjaalie, 1992) and feedback projections from the cerebellum

(Schwarz and Thier, 1999) might play a role. An alternative mechanism to

keep activation by mossy fiber input in different patches roughly equal could

be plasticity of the mossy fiber to granule cell synapse (D'Angelo et al.,

1999). As LTP at this synapse is suppressed by Golgi cell inhibition it may

preferentially enhance transmission at synapses which were not effective in

activating the Golgi cell inhibitory feedback loop and thus boost mossy fibertransmission where it was relatively weak compared to elsewhere.

Conclusions

We propose that mossy fiber input to the cerebellum is coded primarily in

spatial patterns, as reflected by the fractured somatotopy of the receptive

fields in the granular layer. Feedback inhibition by Golgi cells loosely

synchronizes granule cell firing along the parallel fiber beam. Simultaneous

activation of granular layer patches causes synchronized firing of the

activated granule cells and transforms the spatial code into a temporal code

onto the parallel fiber beam. The corticopontine projection contributes by

distributing a (partially) renormalized copy of cortical activity to multiple

patches and possibly by equalizing activity across fibers.

Acknowledgements

We thank Trygve Leergaard and Knut Vassb for assistance with the

preparations of figures, Hugo Cornelis for the necessary software

development and Reinoud Maex and Volker Steuber for careful reading of

the manuscript. This research was funded by EC contract BIO4-CT98-0182,

by The Research Council of Norway, by The Jahre Foundation, by IPA

Belgium (P4/22) and by the Fund for Scientific Research - Flanders (FWO-Vl)

(G.0401.00). EDS is supported by the FWO-Vl.

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E. De Schutter and J.G. Bjaalie- Coding in the Granular Layer of the Cerebellum

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